Depletion forces near a soft surface

We investigate excluded-volume effects in a bidisperse colloidal suspension near a flexible interface. Inspired by a recent experiment by Dinsmore et al. (Phys. Rev, Lett. 80, 409 (1998)), we study the adsorption of a mesoscopic bead on the surface and show that depletion forces could in principle lead to particle encapsulation. We then consider the effect of surface fluctuations on the depletion potential itself and construct the density profile of a polymer solution near a soft interface. Surprisingly we find that the chains accumulate at the wall, whereas the density displays a deficit of particles at distances larger than the surface roughness. This non-monotonic behavior demonstrates that surface fluctuations can have major repercusions on the properties of a colloidal solution. On average, the additional contribution to the Gibbs adsorbance is negative. The amplitude of the depletion potential between a mesoscopic bead and the surface increases accordingly.Comment: 10 pages, 5 figure

A Spectral Bernstein Theorem

We study the spectrum of the Laplace operator of a complete minimal properly immersed hypersurface $M$ in $\R^{n+1}$. (1) Under a volume growth condition on extrinsic balls and a condition on the unit normal at infinity, we prove that $M$ has only essential spectrum consisting of the half line $[0, +\infty)$. This is the case when $\lim_{\tilde{r}\to +\infty}\tilde{r}\kappa_i=0$, where $\tilde{r}$ is the extrinsic distance to a point of $M$ and $\kappa_i$ are the principal curvatures. (2) If the $\kappa_i$ satisfy the decay conditions $|\kappa_i|\leq 1/\tilde{r}$, and strict inequality is achieved at some point $y\in M$, then there are no eigenvalues. We apply these results to minimal graphic and multigraphic hypersurfaces.Comment: 16 pages. v2. Final version: minor revisions, we add Proposition 3.2. Accepted for publication in the Annali di Matematica Pura ed Applicata, on the 05/03/201

Novel Phases in the Field Induced Spin Density Wave State in (TMTSF)_2PF_6

Magnetoresistance measurements on the quasi one-dimensional organic conductor (TMTSF)_2PF_6 performed in magnetic fields B up to 16T, temperatures T down to 0.12K and under pressures P up to 14kbar have revealed new phases on its P-B-T phase diagram. We found a new boundary which subdivides the field induced spin density wave (FISDW) phase diagram into two regions. We showed that a low-temperature region of the FISDW diagram is characterized by a hysteresis behavior typical for the first order transitions, as observed in a number of studies. In contrast to the common believe, in high temperature region of the FISDW phase diagram, the hysteresis and, hence, the first order transitions were found to disappear. Nevertheless, sharp changes in the resistivity slope are observed both in the low and high temperature domains indicating that the cascade of transitions between different subphases exists over all range of the FISDW state. We also found that the temperature dependence of the resistance (at a constant B) changes sign at about the same boundary. We compare these results with recent theoretical models.Comment: LaTex, 4 pages, 4 figure

Electromagnetic suppression of the decay mu --> e+gamma

Due to large QED anomalous dimensions of the electric and magnetic dipole operators, the rate of the rare muon decay mu --> e+gamma is suppressed by the factor [ 1- 8 alpha/pi ln(Lambda/m_mu) ], independent of the physics responsible for the lepton-flavor violation, except for the scale Lambda at which it occurs. For Lambda = 100 -- 1000 GeV, the resulting decrease of the rate amounts to about 12 -- 17 %.Comment: Added analysis of four-fermion operators. Journal versio

Magnetic field-dependent interplay between incoherent and Fermi liquid transport mechanisms in low-dimensional tau phase organic conductors

We present an electrical transport study of the 2-dimensional (2D) organic conductor tau-(P-(S,S)-DMEDT-TTF)_2(AuBr)_2(AuBr_2)_y (y = 0.75) at low temperatures and high magnetic fields. The inter-plane resistivity rho_zz increases with decreasing temperature, with the exception of a slight anomaly at 12 K. Under a magnetic field B, both rho_zz and the in-plane resistivity plane rho_xx show a pronounced negative and hysteretic magnetoresistance with Shubnikov de Haas (SdH)oscillations being observed in some (high quality)samples above 15 T. Contrary to the predicted single, star-shaped, closed orbit Fermi surface from band structure calculations (with an expected approximate area of 12.5% of A_FBZ), two fundamental frequencies F_l and F_h are detected in the SdH signal. These orbits correspond to 2.4% and 6.8% of the area of the first Brillouin zone(A_FBZ), with effective masses F_l = 4.0 +/- 0.5 and F_h = 7.3 +/- 0.1. The angular dependence, in tilted magnetic fields of F_l and F_h, reveals the 2D character of the FS and Angular dependent magnetoresistance (AMRO) further suggests a FS which is strictly 2-D where the inter-plane hopping t_c is virtually absent or incoherent. The Hall constant R_xy is field independent, and the Hall mobility increases by a factor of 3 under moderate magnetic fields. Our observations suggest a unique physical situation where a stable 2D Fermi liquid state in the molecular layers are incoherently coupled along the least conducting direction. The magnetic field not only reduces the inelastic scattering between the 2D metallic layers, but it also reveals the incoherent nature of interplane transport in the AMRO spectrum. The apparent ferromagnetism of the hysteretic magnetoresistance remains an unsolved problem.Comment: 33 pages, 11 figure

Lepton Flavor Violating Process in Bi-maximal texture of Neutrino Mixings

We investigate the lepton flavor violation in the framework of the MSSM with right-handed neutrinos taking the large mixing angle MSW solution in the quasi-degenerate and the inverse-hierarchical neutrino masses. We predict the branching ratio of $\mu \to e+\gamma$ and $\tau \to \mu+\gamma$ processes assuming the degenerate right-handed Majorana neutrino masses. We find that the branching ratio in the quasi-degenerate neutrino mass spectrum is 100 times smaller than the ones in the inverse-hierarchical and the hierarchical neutrino spectra. We emphasize that the magnitude of $U_{e3}$ is one of important ingredients to predict BR($\mu \to e +\gamma$). The effect of the deviation from the complete-degenerate right-handed Majorana neutrino masses are also estimated. Furtheremore, we examine the S_{3\sL}\times S_{3\sR} model, which gives the quasi-degenerate neutrino masses, and the Shafi-Tavartkiladze model, which gives the inverse-hierarchical neutrino masses. Both predicted branching ratios of $\mu\to e+\gamma$ are smaller than the experimantal bound.Comment: Latex file, 38 pages, 10 figures, revised versio

The See-Saw Mechanism, Neutrino Yukawa Couplings, LFV Decays l_i to l_j + gamma and Leptogenesis

The LFV charged lepton decays mu to e + gamma, tau to e + gamma and tau to mu + gamma and thermal leptogenesis are analysed in the MSSM with see-saw mechanism of neutrino mass generation and soft SUSY breaking with universal boundary conditions. The case of hierarchical heavy Majorana neutrino mass spectrum, M_1 10^9 GeV. Considering the natural range of values of the heaviest right-handed Majorana neutrino mass, M_3 > 5*10^{13} GeV, and assuming that the soft SUSY breaking universal gaugino and/or scalar masses have values in the range of few 100 GeV, we derive the combined constraints, which the existing stringent upper limit on the mu to e + gamma decay rate and the requirement of successful thermal leptogenesis impose on the neutrino Yukawa couplings, heavy Majorana neutrino masses and SUSY parameters. Results for the three possible types of light neutrino mass spectrum -- normal and inverted hierarchical and quasi-degenerate -- are obtained.Comment: 25 pages, 9 figures; typos corrected, few clarifying comments and one figure added; version submitted for publicatio

Using Hierarchical Centering to Facilitate a Reversible Jump MCMC Algorithm for Random Effects Models

The first author was supported by a studentship jointly funded by the University of St Andrews and EPSRC, through the National Centre for Statistical Ecology (EPSRC grant EP/C522702/1), with subsequent funding from EPSRC/NERC grant EP/I000917/1.Hierarchical centering has been described as a reparameterization method applicable to random effects models. It has been shown to improve mixing of models in the context of Markov chain Monte Carlo (MCMC) methods. A hierarchical centering approach is proposed for reversible jump MCMC (RJMCMC) chains which builds upon the hierarchical centering methods for MCMC chains and uses them to reparameterize models in an RJMCMC algorithm. Although these methods may be applicable to models with other error distributions, the case is described for a log-linear Poisson model where the expected value λλ includes fixed effect covariates and a random effect for which normality is assumed with a zero-mean and unknown standard deviation. For the proposed RJMCMC algorithm including hierarchical centering, the models are reparameterized by modelling the mean of the random effect coefficients as a function of the intercept of the λλ model and one or more of the available fixed effect covariates depending on the model. The method is appropriate when fixed-effect covariates are constant within random effect groups. This has an effect on the dynamics of the RJMCMC algorithm and improves model mixing. The methods are applied to a case study of point transects of indigo buntings where, without hierarchical centering, the RJMCMC algorithm had poor mixing and the estimated posterior distribution depended on the starting model. With hierarchical centering on the other hand, the chain moved freely over model and parameter space. These results are confirmed with a simulation study. Hence, the proposed methods should be considered as a regular strategy for implementing models with random effects in RJMCMC algorithms; they facilitate convergence of these algorithms and help avoid false inference on model parameters.PostprintPeer reviewe

Proximity effect at superconducting Sn-Bi2Se3 interface

We have investigated the conductance spectra of Sn-Bi2Se3 interface junctions down to 250 mK and in different magnetic fields. A number of conductance anomalies were observed below the superconducting transition temperature of Sn, including a small gap different from that of Sn, and a zero-bias conductance peak growing up at lower temperatures. We discussed the possible origins of the smaller gap and the zero-bias conductance peak. These phenomena support that a proximity-effect-induced chiral superconducting phase is formed at the interface between the superconducting Sn and the strong spin-orbit coupling material Bi2Se3.Comment: 7 pages, 8 figure